Question

Now some information on the Goodweek Tires, Inc. The company only carries debt and

common equity in its balance sheet. The company has 1,000,000 bonds that were issued

some time ago. Each bond has a face value of $100, and is a zero-

coupon bond (that is, the

only cash flow bondholders receive is the repayment of the principal), and is 5 years from

maturity. The price each bond is trading at is $49.24. Regarding equity, the company has

4,000,000 shares outstanding, each one trading today at $80. You can assume that the risk

of the new project mimics quite well the riskiness of all other projects from Goodweek

Tires. The company faces a 40% corporate tax rate, and it has a beta of 1.5. Treasury bonds —a good proxy for a risk free asset —carry a yield of 4.6% per year, and the required

rate of return on the market portfolio is estimated to be 13%.

Answer 1

Current share price, P = $ 80

Nos. of shares outstanding = N = 4,000,000

Market value of equity, V_E = N x P = 4,000,000 x 80 = $ 320 mn

Cost of equity, K_e = Risk free rate + Beta x (Market return - risk free rate) = 4.6% + 1.5 x (13% - 4.6%) = 17.20%

Market value of debt = V_D = Price of each bond x Nos. of bonds = 49.24 x 1 mn = $ 49.24 mn

Pre tax cost of debt, K_d = YTM of the zero coupon bonds = (Face Value / Market Value)^{1 / time to maturity} - 1 = (100 / 49.24)^1/5 - 1 = 15.22%

Tax rate, T = 40%

Hence, WACC = Proportion of debt x K_d x (1 - T) + Proportion of equity x K_e = 49.24 / (49.24 + 320) x 15.22% x (1 - 40%) + 320 / (49.24 + 320) x 17.20% = 16.12%